Fourier Transform Lecture
Digital Signals and Systems are everywhere. Digital 1D signals, 2D signals (images) and 3D signals (video) encompass the vast majority of digital information nowadays in several disciplines:
-Digital Media, Social Media (music, images, video),
-Biomedical Signal/Image Analysis and Diagnosis,
-Autonomous cars, drones, marine vessels, robots
-Big Data Analytics,
-Internet and Communications (media broadcasting, streaming).
-Scientific signal acquisition of any sort, e.g., Remote Sensing, Environment Sensing, Geophysical Prospecting.
Digital Systems can model every aspect of the world, e.g., :
-Financial systems and Engineering
-Biomedical and Biology Systems
-Power plants
-Autonomous Systems and Robotics.
-Neural Networks.
-Social Networks, Complex Networks.
Much confusion exists nowadays in CVML literature, as even mature ML scientists have no background on Signals and Systems and confuse even basic notions, e.g., convolutions and correlations. SS principles are overviewed, while focusing on fast convolution algorithms, particularly on 2D convolution algorithms that are an absolute must for CNN libraries/frameworks and many computer vision tasks.
This lecture overviews the topics of continuous-time periodic signals, signal frequencies and Fourier Transform (FT). Its relation to Laplace transform is presented. Notable FT properties are review: time shift, time scaling, convolution, signal differentiation/integration, energy preservation. Its use in defining Linear Time-Invariant (LTI) continuous-time systems frequency response is presented. Various types of such systems, notably low-pass, high-pass, band-pass are presented with examples (e.g., RC and RLC electric filters).